I jumped over the hole in the ground and then left it to the right. If I fall down in to the bottom, I kill the monster but loose to many points. But I stayed in the second screen as long as I had enough points to break Xerus score.

OK, I don't know what's wrong with my version but I can't jump diagonally, I can only jump straight up. So I couldn't jump that hold, and after killing the monster I couldn't jump over the barrier. I thought there must be some puzzle or trick to get past

Must be I've tried again, still definitely can't diagonal jump. I'm using steem, tos 1.02, and the bladerunners version of the game. Anyway, it doesn't matter, I still got a reasonable score just by killing the enemies on level 2